Isogeometric analysis (IgA) is a well established methodology for the analysis of problems governed by partial differential equations (PDEs); see [1]}, [2]}.
IgA aims to simplify the interoperability between geometric modeling and numerical simulation by constructing a fully integrated framework for computer-aided design (CAD) and finite element analysis (FEA). In its original formulation, IgA uses B-splines, or their rational generalization (NURBS), both to represent the computational domain and to approximate the solution of the PDE that models the problem of interest. The isogeometric paradigm shows important advantages over classical FEA: complicated geometries can be represented more accurately and some common profiles, such as conic sections, are described exactly; the precise geometry description incorporated at the coarsest mesh level can be maintained during mesh refinement through the process of knot insertion; and the inherently high smoothness of B-splines/NURBS allows for a higher accuracy per degree of freedom.
Nevertheless, the above advantages are not a distinguishing property of B-splines/NURBS, and B-splines/NURBS are not a requisite ingredient in IgA.
